CK,
Yeah, it depends on what key you're playing in. I don't have any chord instruments nearby, but my ears tell me (I listened to the recording) that I IV and V are the only chords in the song.
So, key of C: C, F, and G chords
key of G: G, C and D chords
etc.
Honestly I think it would be faster just to try out the chords while listening then to try to write them down in some mutually comprehensible way on this board, so... go for it!

BTW, "Johnnie Come Down to Hilo", as a song divorced from context, is very much in the vein of a minstrel song. So one could easily create an appropriate-sounding instrumental accompaniment. It won't sound like a chanty/work-song, but it will sound like something that makes sense. Same goes for "Hog-eye." The classic minstrel music instruments were banjo, fiddle, bones, and maybe tambourine.